How do you convert degrees to radians?

Multiply by π/180. So 180 degrees is π radians, 90 degrees is π/2, and 1 degree is about 0.01745 radians. Going the other way, multiply radians by 180/π.

Why does mathematics use radians?

Because a radian is defined by the circle itself — the angle where the arc length equals the radius — rather than by an arbitrary division. Calculus formulas for sine and cosine only come out cleanly when angles are in radians.

Why are there 360 degrees in a circle?

Generally traced to Babylonian base-60 arithmetic, and helped by 360 having an unusual number of divisors. It divides evenly by 2, 3, 4, 5, 6, 8, 9, 10 and 12, so common fractions of a circle are whole numbers.

A four-hundredth of a circle, so a right angle is exactly 100 gradians. Tidy for surveying, where it originated, and almost unused anywhere else.

Angle Converter

Convert degrees, radians, gradians, turns and arcminutes.

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About the Angle Converter

Degrees are arbitrary and radians are not, which is why mathematics uses radians and everyone else uses degrees. A radian is the angle subtended when the arc length equals the radius — a definition that comes from the circle itself rather than from a decision — and it is why calculus formulas for sine and cosine only work cleanly in radians.

The 360 in a degree circle is generally traced to Babylonian base-60 arithmetic, helped along by 360 having a great many divisors: it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more, which makes fractions of a circle come out as whole numbers.

The conversion worth memorising is that π radians is 180 degrees, so a right angle is π/2 and a full turn is 2π. Multiplying degrees by π/180 converts one way and by 180/π the other.

Gradians divide the circle into 400 rather than 360, making a right angle exactly 100 — tidy for surveying, and almost unused elsewhere. Arcminutes and arcseconds subdivide a degree by sixty and then sixty again, and are how astronomical positions and latitude are quoted.

How it works

Type a value and choose the units to convert between.
The result updates as you type, with the same value shown in every other unit below.
Jump straight to a direct page for the common conversions listed at the bottom.

Frequently asked questions

How do you convert degrees to radians?: Multiply by π/180. So 180 degrees is π radians, 90 degrees is π/2, and 1 degree is about 0.01745 radians. Going the other way, multiply radians by 180/π.
Why does mathematics use radians?: Because a radian is defined by the circle itself — the angle where the arc length equals the radius — rather than by an arbitrary division. Calculus formulas for sine and cosine only come out cleanly when angles are in radians.
Why are there 360 degrees in a circle?: Generally traced to Babylonian base-60 arithmetic, and helped by 360 having an unusual number of divisors. It divides evenly by 2, 3, 4, 5, 6, 8, 9, 10 and 12, so common fractions of a circle are whole numbers.
What is a gradian?: A four-hundredth of a circle, so a right angle is exactly 100 gradians. Tidy for surveying, where it originated, and almost unused anywhere else.

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